Cellular crystalline metal structures and methods of their manufacture are known, and have been used in a variety of applications, including impact/blast amelioration systems, heat dissipation media, and acoustic isolation applications. These cellular crystalline metal structures typically include sheets of aluminum or other metal and include corrugated metal sheets sandwiched between and bonded to unformed sheets, thereby producing stiff, low density cellular metal structures. The ability of a cellular structure to absorb imparted kinetic energy is directly dependent on the solid material's specific strength, i.e., yield strength divided by density. Accordingly, cellular structures made of low specific strength solids, such as those used in the corrugated metal sheets, do not absorb large amounts of imparted kinetic energy. In addition, the materials used to produce the corrugated metal sheets in these structures exhibit limited solid-state formability, making the corrugated sheets difficult to produce.